To make things simple for yourself, you could just not put the Dihydrocodeine in coffee, get high without worry and call it a day, but you can also do things the hard way if that is your preference!
Codeine Phosphate itself doesn't start to degrade until around 120C if I'm not mistaken. I'm making a possibly foolish assumption that Dihydrocodeine will possess similar properties. In short, the heat from a hot cup of coffee shouldn't be enough to destroy it. In a preliminary sense, I would say that it's probably fine, but again, I think the better option would be just to take the pills.
When I was young and stupid I dumped two 20mg Amphetamine pills into my Mountain Dew. Why? Who the fuck knows. Probably for the same reasons you want to put drugs in coffee. Anyway, I ended up not feeling any effects whatsoever. Maybe it was something in the drink that neutralized the chemical, maybe it stuck to the walls of the bottle. I really have no idea, but I wished that I had just taken the pills. I can tell you that much.